Energy and action flow through the internal wave field: An eikonal approach

Henyey, Frank S.; Wright, Jon; Flatté, Stanley M.

doi:10.1029/jc091ic07p08487

Cited by 330 publications

(268 citation statements)

References 10 publications

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“…which is consistent with the dynamical models introduced by Henyey et al (1986); McComas and Muller (1981). This equation was substituted for term IV in the near-inertial kinetic energy equation (2.6) under the assumption that the dissipation is local in frequency space, i.e.…”

Section: Discussionsupporting

confidence: 54%

Near-inertial and thermal upper ocean response to atmospheric forcing in the North Atlantic Ocean

Silverthorne¹

2010

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Observational and modeling techniques are employed to investigate the thermal and inertial upper ocean response to wind and buoyancy forcing in the North Atlantic Ocean. First, the seasonal kinetic energy variability of near-inertial motions observed with a moored profiler is described. Observed wintertime enhancement and surface intensification of near-inertial kinetic energy support previous work suggesting that near-inertial motions are predominantly driven by surface forcing. The wind energy input into surface ocean near-inertial motions is estimated using the Price-WellerPinkel (PWP) one-dimensional mixed layer model. A localized depth-integrated model consisting of a wind forcing term and a dissipation parameterization is developed and shown to have skill capturing the seasonal cycle and order of magnitude of the near-inertial kinetic energy. Focusing in on wintertime storm passage, velocity and density records from drifting profiling floats (EM-APEX) and a meteorological spar buoy/tethered profiler system (ASIS/FILIS) deployed in the Gulf Stream in February 2007 as part of the CLIvar MOde water Dynamics Experiment (CLIMODE) were analyzed. Despite large surface heat loss during cold air outbreaks and the drifting nature of the instruments, changes in the upper ocean heat content were found in a mixed layer heat balance to be controlled primarily by the relative advection of temperature associated with the strong vertical shear of the Gulf Stream. Velocity records from the Gulf Stream exhibited energetic near-inertial oscillations with frequency that was shifted below the local resting inertial frequency. This depression of frequency was linked to the presence of the negative vorticity of the background horizontal current shear, implying the potential for near-inertial wave trapping in the Gulf Stream region through the mechanism described by Kunze and Sanford (1984). Three-dimensional PWP model simulations show evidence of near-inertial wave trapping in the Gulf Stream jet, and are used to quantify the resulting mixing and the effect on the stratification in the Eighteen Degree Water formation region.

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Section: Discussionsupporting

confidence: 54%

Near-inertial and thermal upper ocean response to atmospheric forcing in the North Atlantic Ocean

Silverthorne¹

2010

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“…This is based on theoretical behavior of internal waves of large vertical wavenumber propagating within a field of internal waves having the Garrett-Munk (GM) internal wave spectrum (Garrett and Munk, 1972;Garrett and Munk, 1975;Munk, 1981). The large-wavenumber waves refract and have evolving vertical wavenumber, intrinsic frequency, group velocity, energy density, etc, and are predicted to dissipate in a manner explained by Henyey, Wright and Flatté (1986). The expression is…”

Section: Data Collection and Data Analysis Methodsmentioning

confidence: 99%

Comparison of deep-ocean finescale shear at two sites along the Mid-Atlantic Ridge

Duda

2006

Deep Sea Research Part II: Topical Studies in Oceanography

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Four drifting floats were used to measure the magnitude of the vertical derivative of horizontal velocity in waters above the rough bathymetry of the Mid Atlantic Ridge. This derivative is typically the dominant component of the velocity gradient (the shear). Two floats were at the site of the Brazil Basin Tracer Release Experiment (BBTRE) in the South Atlantic, and two were near the site of the Guiana Abyssal Gyre Experiment (GAGE) in the North Atlantic. Floats operated for one year except for one BBTRE float which operated for 100 days. Shear was measured over a vertical span of 9.5 m using drag elements that caused the floats to rotate slowly in response to shear. For each float, the first, second and fourth moments of shear were elevated above levels associated with the Garrett-Munk model internal-wave spectrum. Three of the four floats were tracked as they moved over mountainous terrain, allowing shear intensity to be measured as a function of height above the bottom. A deep BBTRE float showed enhancement of rms shear near the bottom. Floats at both areas provided measurements at 2000 m above the bottom, with differing results: The GAGE site had a lower fourth moment of shear (diapycnal diffusivity proxy) than the BBTRE site. However, application of normalization factors accounting for differences between the sites in bottom roughness, latitude-dependent internal-wave dynamics, and tidal current speeds brings the results into agreement.

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“…Nonlinear wave-wave interaction theory has been invoked by McComas and Müller (1981) and Henyey et al (1986) to model the energy flux through the internal wave spectrum to small wavelengths, and thus to turbulence. The energy fluxP to short waves approximately equals the energy flux through the turbulence cascade and the turbulent dissipation rate ε.…”

Section: Basic Dynamic Considerationsmentioning

confidence: 99%

Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

Baumert¹,

Peters

2009

Ocean Sci.

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Abstract. This paper extends a turbulence closure-like model for stably stratified flows into a new dynamic domain in which turbulence is generated by internal gravity waves rather than mean shear. The model turbulent kinetic energy (TKE, K) balance, its first equation, incorporates a term for the energy transfer from internal waves to turbulence. This energy source is in addition to the traditional shear production. The second variable of the new two-equation model is the turbulent enstrophy ( ). Compared to the traditional shear-only case, the -equation is modified to account for the effect of the waves on the turbulence time and space scales. This modification is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean shear when turbulence is produced exclusively by internal waves. This paper is part 1 of a continuing theoretical development. It accounts for mean shear-and internal wavedriven mixing only in the two limits of mean shear and no waves and waves but no mean shear, respectively.The new model reproduces the wave-turbulence transition analyzed by D' Asaro and Lien (2000b). At small energy density E of the internal wave field, the turbulent dissipation rate (ε) scales like ε∼E 2 . This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε∼E 1 . This is observed, for example, in the highly energetic tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.

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Energy and action flow through the internal wave field: An eikonal approach

Cited by 330 publications

References 10 publications

Near-inertial and thermal upper ocean response to atmospheric forcing in the North Atlantic Ocean

Near-inertial and thermal upper ocean response to atmospheric forcing in the North Atlantic Ocean

Comparison of deep-ocean finescale shear at two sites along the Mid-Atlantic Ridge

Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

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